A070806 Primes p such that cototient(totient(p)) = A070556(p) is a power of 2.

3, 5, 7, 13, 17, 29, 97, 113, 193, 257, 449, 509, 769, 7937, 12289, 65537, 114689, 520193, 786433, 7340033, 8388593, 33292289, 33550337, 469762049, 2130706433, 3221225473, 8588886017, 137438691329, 206158430209

Offset

1,1

Links

Table of n, a(n) for n=1..29.

Example

Powers of 2 observable in A070556[this sequence] = {1, 2, 4, 8, 16, 64, 128, 256, 512, 4096, 8192, 32768, 65536, 262144, 524288, ...}. For F(m), Fermat prime:phi[F(m)]=2^m, cototient[2^m]=2^(m-1); if n=113: phi[113]=112, cototient[112]=112-48=64, so 113 is in this sequence.

Mathematica

Do[s= EulerPhi[n]-EulerPhi[EulerPhi[n]]; If[IntegerQ[Log[2, s]]&&PrimeQ[n], Print[n]], {n, 1, 10000000}]

Prog

(PARI) ispow2(n)=n==1<<valuation(n, 2);
forprime(p=2, 4e9, if(ispow2(p-1-eulerphi(p-1)), print1(p", "))) \\ Charles R Greathouse IV, May 17 2011

Crossrefs

Cf. A070556, A051953, A054571, A070807, A070809-A070811.

Sequence in context: A247018 A038929 A242755 * A339506 A178490 A182981

Adjacent sequences: A070803 A070804 A070805 * A070807 A070808 A070809

Keyword

nonn,more

Author

Labos Elemer, May 08 2002

Extensions

a(20)-a(27) from Donovan Johnson, Feb 06 2010

a(28)-a(29) from Charles R Greathouse IV, May 17 2011

Status

approved